By "fiscal theory of monetary policy" I mean a model with standard DSGE ingredients, including inertemporal optimization and market clearing, monetary policy described by interest rate targets, price or other frictions, but closed by fiscal theory, "active" fiscal policy rather than "active" monetary policy.
I aim to build a standard simple but somewhat realistic model of this sort, a parallel to the three equation textbook model that has been part of the new-Keynesian tool kit since the 1990s. I keep the model as simple and standard as possible, so the effect of the innovations one the fiscal side are clearer.
Two parts of the specification are central. First, long-term debt allows the model to produce a negative response of inflation to interest rates. Long-term debt also allows a fiscal shock to result in a protracted inflation, which slowly devalues long term bonds, rather than a price level jump.
Second, and most important, the paper writes down a process for fiscal surpluses in which today's deficits are partially repaid by tomorrow's surpluses. Look quickly at the surplus response functions in my last post. When the government runs a deficit, it reliably runs subsequent surpluses that partially repay some of the accumulated debt. The surplus is not an AR(1)! It has an s-shaped response function.
So if you want a realistic fiscal theory model, you need a surplus with an s-shaped response function, but you need to keep "active" fiscal policy. This combination is the central innovation of the paper.
Active and passive
As a quick reminder for new readers, here's what active and passive mean. Take a really simple model with flexible prices, one period debt, a constant zero real rate, and an interest rate target. The economic model boils down to just
The central bank, by setting the interest rate target, determines expected inflation. But unexpected inflation is not then determined. If fiscal policy is "active" the second equation and the revision to expected surpluses determines unexpected inflation. If fiscal policy is "passive" meaning that the surplus process reacts to unexpected inflation so that the second equation hold for any value of unexpected inflation, then we need another model equation, "active" monetary policy, to determine unexpected inflation.
My goal is to create a model like this, but with sticky prices and output and real interest rate variation, with an empirically sensible specification of surplus (fiscal) policy, that is nonetheless "active" and so closes out the model, determining unexpected inflation.
AR(1) puzzles
So far, many fiscal theory puzzles have come from assuming an AR(1) or similar positively autocorrelated surplus process. An s-shaped surplus process solves the puzzles -- and, conversely, the puzzles provide many different pieces of evidence that the AR(1) is a terrible assumption.
Puzzle 1. Deficits and inflation. An AR(1) surplus predicts that deficits come with substantial inflation. By and large we see the opposite sign, less inflation with deficits in a recession and vice versa, and little reliable correlation. An s-shaped surplus process solves the puzzle.
I'll illustrate with a constant interest rate, short term debt version of the model. The simple FTPL is
How can we cure this puzzle? Well, the key assumption is that a shock to surpluses today raises forecasts of surpluses in the future -- all the
Puzzle 2: Damningly, the AR(1) or other positively autocorrelated surplus predicts that a higher surplus today raises the value of the debt tomorrow, just as a higher dividend today leads to a higher stock price. A higher surplus forecasts higher future surpluses, and the value of the debt is the present value of subsequent surpluses. Yet higher surpluses in the data unequivocally pay down the value of the debt, and deficits result in more debt, as pointed out by Canzoneri, Cumby and Diba.
A surplus process with an s-shaped moving average solves the puzzle. A higher surplus today corresponds to a decrease in present value of subsequent surpluses, and hence a decline in the value of debt.
Puzzle 3: With AR(1) or positively autocorrelated surpluses, all deficits are paid for by devaluing outstanding debt via inflation (or default), and none are paid for by selling new debt. Running a deficit involves selling less real debt. With an s-shaped moving average, deficits are financed by borrowing.
Bond buyers will only hand over resources to finance today's deficits if they are convinced that the bonds will be paid off by future surpluses, essentially proving that bond buyers think the surplus process is s-shaped.
Puzzle 4: Models with positively autocorrelated surpluses predict that the risk and hence expected return of government bonds should be huge. The s-shaped surplus process solves this puzzle, allowing even risk free government debt.
Since all deficits are paid by unexpectedly inflating away bonds, since
An s-shaped surplus process resolves the puzzle. When the ``dividend,'' surplus, falls, the ``price,''
present value of subsequent surpluses, rises. The overall return need not move at all, nor offer a positive compensation for risk. Stock dividends don't follow an s-shaped process. Government deficits and surpluses do.
The standard specification of fiscal policy is
The model
OK, hold your breath. Here is the model. If this is too much in one bite, read the paper which builds up to the model bit by bit. (The whole point of this blog post is to get you to read the paper after all!) Here we'll just sit down to the main course without appetizers.
The first two equations are the standard intertemporal substitution (IS) and forward-looking Phillips curve. The third equation is a standard interest rate policy rule.
The surplus
One way to think of the difference between
The parameter
The
Responses
Here are the responses to a fiscal policy shock, a unit
This first response has no policy rules -- the
The fiscal shock leads to a AR(1) pattern of inflation, and as a consequence of the standard Phillips curve an output expansion. With no policy response, interest rates stay put. Now, let's add a monetary and fiscal policy response.
The rise in inflation and output provokes a rise in interest rate. And the initial inflation devalues long term bonds
Big points: 1) Fiscal theory does not just imply big price level jumps in response to fiscal shocks. Fiscal theory rather naturally here leads to a very long and drawn out inflation in response to a fiscal shock. 2) Endogenous monetary and fiscal policy responses also draw out and buffer the response to a fiscal shock.
Here is the response to a monetary policy shock
Surpluses are not constant, because they react to the rise in value of debt that comes from higher real interest rates, represented by the difference between the interest rate and inflation lines. Bond returns follow the expectations hypothesis, mirroring the interest rate with a one period lag, except in the first period. A rise in interest rates leads to a big ex-post decline in bond prices.
Last and most of all, here is the response to monetary policy with policy rules in place.
The interest rate no longer follows its shock. Lower output and inflation bring down the actual interest rate. The monetary policy induced recession now has a deficit too, as the surplus responds to lower output and inflation. Inflation and output still decline in response to the monetary policy shock.
There is a lot more going on here. Real interest rate variation leads to discount rate effects, for example. But I what to whet your appetite to read the paper.
The goal: a really simple baseline fiscal theory of monetary policy model that produces reasonable responses to fiscal and monetary policy. We have drawn out inflation in response to fiscal shocks, not a price level jump; we have lower inflation and output in response to monetary policy not instant Fisherism; and all the AR(1) puzzles are solved. It seems a good place to start. And, for today, to stop.
(Note: this post uses Mathjax to display equations, which is not working perfectly.)
The weakness of the postulated model and its variants, apart from the complexity of the presentation, lies in the definition of the variable s which represents but is not the real value of the government's primary surplus (deficit). In the paper, you describe two different definitions of the variable s: one is defined as the quotient of the real primary surplus and the steady-state value of government debt without defining how that steady-state value is obtained or becomes known, and the other is defined as the quotient of real primary surplus and current gross domestic product (GDP or Y, depending on one's choice of terminology) but GDP (or Y) is a function of, for instance, x, log excess production capacity in the economy and other factors in the model. One can understand why the variable s is preferred to, say, log("real primary surplus") because the value of "real primary surplus" can take any value along the real number line, including non-positive values, which would destroy the log-linearization construction of the model, but is this justified when the quotients' denominators are themselves a variable of the model? This is perhaps a question to be addressed by a student of econometrics.
ReplyDeleteThe subject matter is of great interest without doubt to those who invest in government securities (and in common stocks to a lesser extent). It is an area of study that presents great challenges to the theoretical economist. For the practitioner, the greatest aid would be found in the development of a less rigorous but robust understanding of how the principal variables of interest affect the price level. Knowledge of the basic interactions between the variables and future outcomes is perhaps all that the practitioner can ever hope to achieve, but having achieved that she would be better able to anticipate future moves in the market to the benefit of her client.
ReplyDeleteIn reading the model, I cannot help but distinguish between a state variable, say, X(t), from the expectation at time t of the one-period ahead value X(t+1), i.e., E(X(t+1)|I(t)) where I(t) is the information set at period t. In the formulation of the model, X(t) appears to be the dependent (endogenous) variable whereas E(X(t+1)|I(t)) is the independent (exogenous) variable, as I see it. I arrive at this notion based on the line of thinking that the expectation is formed prior to the realization and that expectation can only have weight if it is the composite expectation of the market participants. Thus, X(t) is determined, in part, by E(X(t+1)|I(t)) -- i.e., the businessman sets his capacity level based on an expectation of business conditions in the period ahead. Perhaps this is a bit fanciful on my part, but it seems to fit experience--we make investment decisions based on expectations of the future state of the economy, not the state of the economy as it was in the past (near or distant).
ReplyDeleteI have threat of seigniorage tax. When investors see the Fed engage in QE then they know seigniorage income to government increases. This is a tax on the bond industry, the bond industry responds with more excess reserves which avoid the tax. Thus we get excess reserves to match treasuries held. The mechanism is fiscal, sure, via Treasury and the primary dealers, they hold the lag.
ReplyDeleteI'd like to really congratulate you on effectively breaking through the "levels" barrier.
ReplyDeleteTypically, economists and financial professors work with rates, while ignoring any sort of "level" effect. There are volumes of research on what determines stock returns, but almost no research on what determines stock valuations.
Similarly, there is a lot of research on GDP growth rates, inflation rates, tax rates, and interest rates. Yet, there is almost no research on what drives future total debt, money supply, total tax revenue, and national wealth.
What you've discovered is that there's an obvious (in 2020) error-correction that happens with all financial accounts over time. The fundamental equilibria in economics are not equilibria of rates, but equilibria of levels.
This is the problem that governments grapple with:
ReplyDelete- A decrease in wealth will force people to work more, thus increasing Y.
- An increase in wealth will enable people to buy more, thus increasing Y.
Because governments earn revenue based on Y, not on wealth, they can't figure out whether to make people more or less wealthy.